Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some setX, which is transitive, antisymmetric, and total (this relation is denoted here by infix ≤). A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain.

If X is totally ordered under ≤, then the following statements hold for all a, b and c in X:

Antisymmetry eliminates uncertain cases when both a precedes b and b precedes a. A relation having the property of "totality" means that any pair of elements in the set of the relation are comparable under the relation. This also means that the set can be diagrammed as a line of elements, giving it the name linear.Totality also implies reflexivity, i.e., a ≤ a. Therefore, a total order is also a partial order. The partial order has a weaker form of the third condition. (It requires only reflexivity, not totality.) An extension of a given partial order to a total order is called a linear extension of that partial order.

Chain (unit)

A chain (ch) is a unit of length. It measures 66 feet, or 22 yards, or 100 links, or 4 rods (20.1168 m). There are 10 chains in a furlong, and 80 chains in one statute mile. An acre is the area of 10 square chains (that is, an area of one chain by one furlong). The chain has been used for several centuries in Britain and in some other countries influenced by British practice.

By extension, chainage (running distance) is the distance along a curved or straight survey line from a fixed commencing point, as given by an odometer.

Origin

The chain was commonly used with the mile to indicate land distances and in particular in surveying land for legal and commercial purposes. Starting in the 19th centary, the chain was used as a sub division with the mile to show distances between railway stations, tunnels and bridges. In medieval times, local measures were commonly used, and many units were adopted that gave manageable units; for example the distance from London to York could be quoted in inches, but the resulting huge number would be unmemorable. The locally used units were often inconsistent from place to place.

Chain (Paul Haig album)

Chain was Edinburgh musician Paul Haig's third album and was released in May 1989 on Circa Records, a subsidiary of Virgin Records. Chain, which Haig financed himself, was recorded and completed in 1988, but it sat on the shelf after the normally accommodating Les Disques Du Crepuscule decided not to take up the option of releasing it. The album was co-produced by long-time Haig cohort, Alan Rankine, instrumentalist with celebrated Dundee band, The Associates. There was another Associates connection on the album - the track "Chained" was written by Haig's good friend, Billy Mackenzie. Haig returned the favour and gave Mackenzie the track "Reach The Top" for his album The Glamour Chase, which after many years in limbo was finally released in 2002.

One single, "Something Good", was taken from the album, but much to Circa's disappointment, neither the single nor the album sold in great numbers.

Progressive Party (United States, 1912)

The party also became known as the Bull Moose Party after journalists quoted Roosevelt saying "I feel like a bull moose" shortly after the new party was formed.

Birth of a new party

Roosevelt left office in 1909. He had selected Taft, his Secretary of War, to succeed him as presidential candidate, and Taft easily won the 1908 presidential election. Roosevelt became disappointed by Taft's increasingly conservative policies. Taft upset Roosevelt when he used the Sherman Anti-Trust Act to break up U.S. Steel. During his own presidency, Roosevelt had approved J.P. Morgan-owned U.S. Steel as a "good" trust. They became openly hostile, and Roosevelt decided to seek the presidency.

Roosevelt entered the campaign late, as Taft was already being challenged by progressive leader Senator Robert La Follette of Wisconsin.

In 2003 the party re-changed its name to the Progressive Party. PP has also supported the Workers' Party-led government since 2003.

At the parliamentary elections, held in October 2006, the party won 42 of the 513 seats in the chamber of deputies, and it has 1 of the 81 seats in the Senate. At the 2010 elections, PP won 41 seats in the Chamber of Deputies, and made gains in the Senate for a total of 5 seats. It lost an extremely close gubernatorial runoff in Roraima to the PSDB, and won no state governorships.